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04/12/2013 PHY 712 Spring 2013 -- Lecture 32 1
PHY 712 Electrodynamics11-11:50 AM MWF Olin 107
Plan for Lecture 32:
Read material from Chap. 13 & 15
1. Cherenkov radiation
2. Bremsstrahlung
04/12/2013 PHY 712 Spring 2013 -- Lecture 32 2
04/12/2013 PHY 712 Spring 2013 -- Lecture 32 3
04/12/2013 PHY 712 Spring 2013 -- Lecture 32 4
References for notes: Glenn S. Smith, An Introduction to Electromagnetic Radiation (Cambridge UP, 1997), Andrew Zangwill, Modern Electrodynamics (Cambridge UP, 2013)
Cherenkov radiation Discovered ~1930; bluish light emitted by energetic
charged particles traveling within dielectric materials
qqc
04/12/2013 PHY 712 Spring 2013 -- Lecture 32 5
JAActc
tc
41
41units)Gaussian cgsgauge;(Lorentzty permeabiliand
ty permittivihavingmateriala within equationspotentialsMaxwell'
2
2
22
2
2
22
ttqt
tqtt
q
q
RrRrJ
RrrR
,
,:ory on trajectmovingparticlecharged:Source
q
Rq(t)
04/12/2013 PHY 712 Spring 2013 -- Lecture 32 6
Liénard-Wiechert potential solutions:
n
rr
nn
rqrn
rqr
rnr
n
rnr
ctRtt
nccc
ct
t
ttttR
qt
ttRqt
,
1,
Rβ
RrRRβ
βrA
Rβr
04/12/2013 PHY 712 Spring 2013 -- Lecture 32 7
vtr2 vtr3vtr1 vt
r
R(t)=r-vt
q
v(t-tr)
04/12/2013 PHY 712 Spring 2013 -- Lecture 32 8
1
1
2
:for equation Quadratic
algebraSome
2
222
2222
n
nnnnr
nrnnrnnr
nr
rrnr
rrr
tRttctt
cttcttttRctt
cttttttRcttttttt
tt
βRβR
βR
vRvRvrR
vrR
04/12/2013 PHY 712 Spring 2013 -- Lecture 32 9
1
sin1cos
111coscos
cos:Denote1
1
continued--algebraSome
2
22
2
22
2
222
n
nn
n
nnnr
nn
n
nnnnr
tttR
tttRctt
ttRt
tRttctt
q
βR
βRβR
04/12/2013 PHY 712 Spring 2013 -- Lecture 32 10
1
sin1cos
1sinwhere2
1in0cos:1iffor solutionsrealfor Conditions
1sin1cos
continued--algebraSome
2
22
2
22
n
nnnr
n
nCC
n
n
n
nnnr
tttRctt
vct
tstt
tttRctt
qqq
qqq
04/12/2013 PHY 712 Spring 2013 -- Lecture 32 11
vtr2 vtr3vtr1 vt
r
R(t)=r-vtq
v(t-tr)
vtr2 vtr3vtr1 vtr4 vt
cn(t-tr) qc
04/12/2013 PHY 712 Spring 2013 -- Lecture 32 12
Liénard-Wiechert potential solutions for this case:
1
sin1cos
,
1,
2
22
n
nnrnr
rnnrqr
rnr
n
rnr
tttRtRctt
ttctttttR
qt
ttRqt
βRRrRRβ
βrA
Rβr
04/12/2013 PHY 712 Spring 2013 -- Lecture 32 13
Liénard-Wiechert potential solutions -- continued:
ttt
tc
tt
tttR
qt
tttR
qt
C
n
n
C
n
,,
,1,,
:fieldsmagneticandElectric
coscossin1
2,
coscossin1
12,
22
22
rArB
rArrE
βrA
r
04/12/2013 PHY 712 Spring 2013 -- Lecture 32 14
Liénard-Wiechert potential solutions -- continued:
tttt
tttR
tq
tttR
tqt
n
C
n
nn
C
n
n
,ˆsin,
coscossin1
/1ˆ2
coscossin1
1ˆ2,
2/1222
2/12
2/3222
2
rEθrB
R
RrE
04/12/2013 PHY 712 Spring 2013 -- Lecture 32 15
c
2
22
22
1
....clearsdust When the)0(
12sin1
)0(coscos
vc
ddId
Rtc
t
Rtct
n
nnn
n
nC
vtr2 vtr3vtr1 vtr4 vt
cn(t-tr) R 0
